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The Quadratic Assignment Problem (QAP) is an optimization problem that deals with assigning a set of facilities to a set of locations, considering the pairwise distances and flows between them.
The problem is to find the assignment that minimizes the total cost or distance, taking into account both the distances and the flows.
The distance matrix and flow matrix, as well as restrictions to ensure each facility is assigned to exactly one location and each location is assigned to exactly one facility, can be used to formulate the QAP as a quadratic objective function.
The QAP is a well-known example of an NP-hard problem, which means that for larger cases, computing the best solution might be difficult. As a result, many algorithms and heuristics have been created to quickly identify approximations of answers.